1. Field of the Invention
The present invention relates to a method of simulating rolling tire capable of precisely predicting energy loss.
2. Description of the Related Art
A rolling resistance of a tire largely exerts an influence upon fuel economy of a vehicle, and it is conceived that a contribution rate of the rolling resistance to the fuel economy is about 10%. Thus, in order to improve the fuel performance of a vehicle, it is important to analyze the rolling resistance of a tire. To evaluate the rolling resistance of a tire, it is conventionally necessary to actually prototype a tire and test the tire. However, such a method requires enormous amounts of time, costs and labor. Therefore, it is required to further enhance the developing efficiency.
In “Development of Analyzing Technique of Rolling Resistance of Tire” (the society of automotive engineers of Japan, academic session preprint 852074, written by Youichi KOBAYASI, et al) (document 1, hereinafter), there is described a static analysis for analyzing the rolling resistance by a tire model into contact with a road model without rolling. In this analysis, energy loss of an element of a viscoelastic material of the tire model is calculated using a following equation:Ui×Vi×tan δi
wherein                Ui represents energy density Ui or the element,        Vi represents volume of the element and        tan δi represents loss tangent defined for the element.        
Further, in “Tire Science and Technology, TSTCA, vol. 27, No. 1 January-March 1999 P. 22 (Tire Temperature and Rolling Resistance Prediction with Finite Element Analysis) (document 2, hereinafter), there is also described a static analysis of tire model. In this analysis, energy loss per unit volume of the tire model is calculated mainly using “dynamic loss modulus G” and an amplitude of strain.
According to these two methods, the distribution of strain when the tire model is gently brought into contact with a road surface is regarded as the variation of strain received by arbitrary element when the tire rotates once. Therefore, according to the methods described in the two documents, it is necessary to use such a tire model that the cross section shape and material properties of whole elements are uniform in the tire circumferential direction. Thus, if the tire model has a tread portion provided with a lateral groove extending in the axial direction of the tire and the cross section shape of the tire is not continuous in the tire circumferential direction, or if the tire has material properties which are varied in the circumferential direction, precise energy loss can not be calculated by the above methods.
In the document 1, strain energy density is used to calculate the energy loss. If the strain energy density is used, since the direction of deformation of each element of the tire model is not taken into consideration, a logical contradiction arises frequently. As shown in FIG. 14 for example, when strain ε is in an element “e” generated in the direction X at time point A and strain ε is generated in the direction y at next time point B, both strains are the same strain energies and no energy loss is generated according to the strain energy system. In the reality, however, since the direction of deformation is varied, energy loss is generated.
According to the document 2, the amplitude of strain is used to calculate the energy loss. However, this method has a serious problem that since attention is merely paid to the maximum amplitude of strain, when there are two or more peaks in hysteresis of strain as shown in FIG. 7 for example (such a case is generated frequently), the energy loss is calculated smaller than the actual value.